This study makes a first attempt at a detailed estimation of the background radioactivity level and its distribution at the Sinop nuclear power plant site. The activity concentration levels of Ra-226, Th-232, K-40 and Cs-137 radionuclides in soil samples collected from 88 locations around Sinop Province, Turkey, in November 2016, were measured using gamma spectrometry. The distributions of radionuclide levels obtained from the results were evaluated using a geostatistical method, and the estimated radiation levels were determined using the ordinary kriging (OK) method, which is the best linear unbiased estimator (BLUE) for unmeasured points. Estimates of distribution results were evaluated using cross-validation diagrams, and it was shown that the OK method could predict radiological distributions for appropriate criteria. Finally, using the kriging parameters, distributions of radiation levels for the entire work area were mapped at a spatial resolution of 100 x 100 m(2). These maps show that the natural radionuclides (Ra-226, Th-232 and K-40) are distributed at higher levels to the southeast of Sinop than in the other regions, and the activity of an artificial radionuclide (Cs-137) is high in the interior and northern sections.